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<h2 title="Class mxUnionFind" class="title">Class mxUnionFind</h2>
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<pre>public class <span class="typeNameLabel">mxUnionFind</span>
extends java.lang.Object</pre>
<div class="block">Implements a union find structure that uses union by rank and path
compression. The union by rank guarantees worst case find time of O(log N),
while Tarjan shows that in combination with path compression (halving) the
average time for an arbitrary sequence of m >= n operations is
O(m*alpha(m,n)), where alpha is the inverse of the Ackermann function,
defined as follows:
<code>alpha(m,n) = min{i &gt;= 1 | A(i, floor(m/n)) &gt; log n} for m &gt;= n &gt;= 1</code>
Which yields almost constant time for each individual operation.</div>
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<td class="colFirst"><code>class&nbsp;</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a></span></code>
<div class="block">A class that defines the identity of a set.</div>
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<td class="colFirst"><code>protected java.util.Map&lt;java.lang.Object,<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&gt;</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../com/mxgraph/analysis/mxUnionFind.html#nodes">nodes</a></span></code>
<div class="block">Maps from elements to nodes</div>
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<td class="colOne"><code><span class="memberNameLink"><a href="../../../com/mxgraph/analysis/mxUnionFind.html#mxUnionFind-java.lang.Object:A-">mxUnionFind</a></span>(java.lang.Object[]&nbsp;elements)</code>
<div class="block">Constructs a union find structure and initializes it with the specified
elements.</div>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../com/mxgraph/analysis/mxUnionFind.html#differ-java.lang.Object-java.lang.Object-">differ</a></span>(java.lang.Object&nbsp;a,
java.lang.Object&nbsp;b)</code>
<div class="block">Returns true if element a and element b are not in the same set.</div>
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<td class="colFirst"><code><a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a></code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../com/mxgraph/analysis/mxUnionFind.html#find-com.mxgraph.analysis.mxUnionFind.Node-">find</a></span>(<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&nbsp;node)</code>
<div class="block">Returns the set that contains <code>node</code>.</div>
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<td class="colFirst"><code><a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a></code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../com/mxgraph/analysis/mxUnionFind.html#getNode-java.lang.Object-">getNode</a></span>(java.lang.Object&nbsp;element)</code>
<div class="block">Returns the node that represents element.</div>
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<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../com/mxgraph/analysis/mxUnionFind.html#union-com.mxgraph.analysis.mxUnionFind.Node-com.mxgraph.analysis.mxUnionFind.Node-">union</a></span>(<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&nbsp;a,
<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&nbsp;b)</code>
<div class="block">Unifies the sets <code>a</code> and <code>b</code> in constant time
using a union by rank on the tree size.</div>
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<h3>Methods inherited from class&nbsp;java.lang.Object</h3>
<code>clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait</code></li>
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<h4>nodes</h4>
<pre>protected&nbsp;java.util.Map&lt;java.lang.Object,<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&gt; nodes</pre>
<div class="block">Maps from elements to nodes</div>
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<h4>mxUnionFind</h4>
<pre>public&nbsp;mxUnionFind(java.lang.Object[]&nbsp;elements)</pre>
<div class="block">Constructs a union find structure and initializes it with the specified
elements.</div>
<dl>
<dt><span class="paramLabel">Parameters:</span></dt>
<dd><code>elements</code> - </dd>
</dl>
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<h4>getNode</h4>
<pre>public&nbsp;<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&nbsp;getNode(java.lang.Object&nbsp;element)</pre>
<div class="block">Returns the node that represents element.</div>
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<h4>find</h4>
<pre>public&nbsp;<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&nbsp;find(<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&nbsp;node)</pre>
<div class="block">Returns the set that contains <code>node</code>. This implementation
provides path compression by halving.</div>
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<h4>union</h4>
<pre>public&nbsp;void&nbsp;union(<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&nbsp;a,
<a href="../../../com/mxgraph/analysis/mxUnionFind.Node.html" title="class in com.mxgraph.analysis">mxUnionFind.Node</a>&nbsp;b)</pre>
<div class="block">Unifies the sets <code>a</code> and <code>b</code> in constant time
using a union by rank on the tree size.</div>
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<h4>differ</h4>
<pre>public&nbsp;boolean&nbsp;differ(java.lang.Object&nbsp;a,
java.lang.Object&nbsp;b)</pre>
<div class="block">Returns true if element a and element b are not in the same set. This
uses getNode and then find to determine the elements set.</div>
<dl>
<dt><span class="paramLabel">Parameters:</span></dt>
<dd><code>a</code> - The first element to compare.</dd>
<dd><code>b</code> - The second element to compare.</dd>
<dt><span class="returnLabel">Returns:</span></dt>
<dd>Returns true if a and b are in the same set.</dd>
<dt><span class="seeLabel">See Also:</span></dt>
<dd><a href="../../../com/mxgraph/analysis/mxUnionFind.html#getNode-java.lang.Object-"><code>getNode(Object)</code></a></dd>
</dl>
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